Two bodies of masses 2 kg and 8 kg are separated by a distance of 9 m . The point where the resultant gravitational field intensity is zero is at a distance of

Question

Two bodies of masses 2 kg and 8 kg are separated by a distance of 9 m . The point where the resultant gravitational field intensity is zero is at a distance of (A) 4.5m from each mass (B) 6 m from 2 kg (C) 6m from 8kg (D) 2.5m from 2kg

Tardigrade Admin · Accepted Answer

If x is the distance of point on the line joining the two masses from mass m2â² where gravitational field intensity is zero, then (G m/(r - x)2)=(G m2/x2) or (2/(9 - x)2)=(8/x2) or (1/9 - x)=(2/x) On solving, x=6 m

Q. Two bodies of masses $2 k g$ and $8 k g$ are separated by a distance of $9 m$ . The point where the resultant gravitational field intensity is zero is at a distance of

$4.5 m$ from each mass

$6 m$ from $2 k g$

$6 m$ from $8 k g$

$2.5 m$ from $2 k g$

If $x$ is the distance of point on the line joining the two masses from mass $m_{2}'$ where gravitational field intensity is zero, then
$\frac{G m}{( r - x ) ^{2}} = \frac{G m _{2}}{x ^{2}}$ or $\frac{2}{( 9 - x ) ^{2}} = \frac{8}{x ^{2}}$
or $\frac{1}{9 - x} = \frac{2}{x}$
On solving, $x = 6 m$

Q. Two bodies of masses 2kg and 8kg are separated by a distance of 9m . The point where the resultant gravitational field intensity is zero is at a distance of

4.5m from each mass

6m from 2kg

6m from 8kg

2.5m from 2kg